We propose a coarse-grained model for polymer chains and polymer networks based on the meso-scale dynamics. The model takes the internal degrees of freedom of the constituent polymer chains into account using memory functions and colored noises. We apply our model to dilute polymer solutions and polymer networks. A numerical simulation on a dilute polymer solution demonstrates the validity of the assumptions on the dynamics of our model. By applying this model to polymer networks, we find a transition in the dynamical behavior from an isolated chain state to a network state.
A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific polymer and reflect the underlying atomistic details to some extent, and those which retain only the most basic features of a polymer chain (chain connectivity, short-range excluded-volume interactions, etc.). In this review we mainly focus on the second class of generic polymer models, while the first class of specific coarse-grained models is only touched upo…
Reducing the complexity of cross-linked polymer networks by preserving their main macroscale properties, is key to understanding them, and a crucial issue is to relate individual properties of the polymer constituents to those of the reduced network. Here we study polymer networks in a good solvent, by considering star polymers as their unit elements, and first quantify the interaction between their centers of masses. We then reduce the complexity of a network by replacing sets of its bridged star polymers by equivalent effective soft particles with dense cores. Our coarse graining allows us t…
The self- and mutual-avoiding walk used in conventional lattice models for polymeric systems requires that all lattice sites, polymer segments, and solvent molecules (unoccupied lattice sites) have the same volume. This incorrectly accounts for the solvent entropy (i.e., size ratio between polymer segments and solvent molecules), and also limits the coarse-graining capability of such models, where the invariant degree of polymerization controlling the system fluctuations is too small (thus exaggerating the system fluctuations) compared to that in most experiments. Here we show how to properly …
Based on the wormlike chain model, a coarse-grained description of the nonlinear dynamics of a weakly bending semiflexible polymer is developed. By means of a multiple scale perturbation analysis, a length-scale separation inherent to the weakly-bending limit is exploited to reveal the deterministic nature of the spatio-temporal relaxation of the backbone tension and to deduce the corresponding coarse-grained equation of motion. From this partial integro-differential equation, some detailed analytical predictions for the non-linear response of a weakly bending polymer are derived in an accompa…
We investigated the elongational flows of the weakly entangled linear polymer melt using a coarse-grained molecular dynamics simulation. We extended the uniform extensional flow (UEF) method developed by Nicholson and Rutledge (D. A. Nicholson and G. C. Rutledge, J. Chem. Phys., 145, 244903 (2016)) for application to Langevin dynamics. We succeeded in observing the elongational viscosity of the weakly entangled linear polymer melt from the equilibrium state to the steady state using the extended UEF method, whereas the conventional rectangular parallelepiped shape technique for extensional flo…
We compare different coarse-grained models for star polymers. We find that phenomenological models inspired by the Daoud-Cotton model reproduce quite poorly the thermodynamics of these systems, even if the potential is assumed to be density dependent, as done in the analysis of experimental results. We also determine the minumum value fc of the functionality of the star polymer for which a fluid-solid transition occurs. By applying the Hansen-Verlet criterion we find 35 < fc < 40. This result is confirmed by an analysis based on the modified (reference) hypernetted chain method and is qualitat…
A coarse-graining strategy, previously developed for polymer solutions, is extended here to mixtures of linear polymers and hard-sphere colloids. In this approach groups of monomers are mapped onto a single pseudoatom (a blob) and the effective blob-blob interactions are obtained by requiring the model to reproduce some large-scale structural properties in the zero-density limit. We show that an accurate parametrization of the polymer-colloid interactions is obtained by simply introducing pair potentials between blobs and colloids. For the coarse-grained model in which polymers are modelled as…
Numerically optimized reduced descriptions of macromolecular liquids often present thermodynamic inconsistency with atomistic level descriptions even if the total correlation function, i.e. the structure, appears to be in agreement. An analytical expression for the effective potential between a pair of coarse-grained units is derived starting from the first-principles Ornstein-Zernike equation, for a polymer liquid where each chain is represented as a collection of interpenetrating blobs, with a variable number of blobs, $n_b$, of size $N_b$. The potential is characterized by a long tail, slow…
To study the cooling behavior and the glass transition of polymer melts in bulk and with free surfaces a coarse-grained weakly semi-flexible polymer model is developed. Based on a standard bead spring model with purely repulsive interactions an attractive potential between non-bonded monomers is added, such that the pressure of polymer melts is tuned to zero. Additionally, the commonly used bond bending potential [Everaers et al., Science 303, 823 (2004)] controlling the chain stiffness is replaced by a new bond bending potential. For this model, we show that the Kuhn length and the internal d…
Viscosity overshoot of entangled polymer melts has been observed under shear flow and uniaxial elongational flow, but has never been observed under biaxial elongational flow. We confirmed the presence of viscosity overshoot under biaxial elongational flows observed in a mixed system of ring and linear polymers expressed by coarse-grained molecular dynamics simulations. The overshoot was found to be more pronounced in weakly entangled melts. Furthermore, the threshold strain rate $\dot{\varepsilon}_{\rm th}$ distinguishing linear and nonlinear behaviors was found to be dependent on the linear c…
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density σg, the length ns the grafted side chains and their chemical nature fully determines the properties of each macromolecule, such as its elasticity and its folding behaviour. Typically, experimental bottle brushes are systems made of tens of thousands of monomeric units, rendering a computational approach extremely expensive, especially in the case of bottle brush solutions. A proper coarse graining description of these macromolecules thus appears essential…
We present a theoretical approach to scale the artificially fast dynamics of simulated coarse-grained polymer liquids down to its realistic value. As coarse-graining affects entropy and dissipation, two factors enter the rescaling: inclusion of intramolecular vibrational degrees of freedom, and rescaling of the friction coefficient. Because our approach is analytical, it is general and transferable. Translational and rotational diffusion of unentangled and entangled polyethylene melts, predicted from mesoscale simulations of coarse-grained polymer melts using our rescaling procedure, are in qu…
Soft nanocomposites represent both a theoretical and an experimental challenge due to the high number of the microscopic constituents that strongly influence the behaviour of the systems. An effective theoretical description of such systems invokes a reduction of the degrees of freedom to be analysed, hence requiring the introduction of an efficient, quantitative, coarse-grained description. We here report on a novel coarse graining approach based on a set of transferable potentials that quantitatively reproduces properties of mixtures of linear and star-shaped homopolymeric nanocomposites. By…
We introduce a kinetic model of coarsening of transient polymer networks during the intermediate stages of phase separation in polymer systems. The model explicitly takes into account the effect of the connectivity of polymer chains. We show that during the intermediate stages the size of the droplet grows according to an unusual coarsening law $R \sim t^{1/(d + 3)}$. When the network structure breaks up, the coarsening law may cross over to $R \sim \ln t^{-1}$, until only at very late stages the Lifshitz-Slyozov coarsening law $R \sim t^{1/3}$ is recovered.
We show how to coarse grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-points or end-points of the polymers. We also show how to extend these methods to polymers in poor solvents and mixtures of polymers. Treating polymers as soft colloids can greatly speed up the simulation of complex many-polymer systems, including polymer-colloid mixtures.
We consider a coarse-grained (CG) model with pairwise interactions, suitable to describe low-density solutions of star-branched polymers of functionality $f$. Each macromolecule is represented by a CG molecule with $(f+1)$ interaction sites, which captures the star topology. Potentials are obtained by requiring the CG model to reproduce a set of distribution functions computed in the microscopic model in the zero-density limit. Explicit results are given for $f=6,12$ and $40$. We use the CG model to compute the osmotic equation of state of the solution for concentrations $c$ such that $Φ_p = c…
The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the …
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To…
We discuss the reliability of integral-equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterized by mutually interacting soft and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behavior when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we fin…
We develop a coarse-grained particle-based model to simulate membranes with nematic liquid-crystal order. The coarse-grained particles form vesicles which, at low temperature, have orientational order in the local tangent plane. As the strength of coupling between the nematic director and the vesicle curvature increases, the vesicles show a morphology transition from spherical to prolate and finally to a tube. We also observe the shape and defect arrangement around the tips of the prolate vesicle.
We critically discuss and review the general ideas behind single- and multi-site coarse-grained (CG) models as applied to macromolecular solutions in the dilute and semi-dilute regime. We first consider single-site models with zero-density and density-dependent pair potentials. We highlight advantages and limitations of each option in reproducing the thermodynamic behavior and the large-scale structure of the underlying reference model. As a case study we consider solutions of linear homopolymers in a solvent of variable quality. Secondly, we extend the discussion to multi-component systems pr…
Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k --> 0 limit, c0. A numerical solution to the PRISM integral equati…
Coarse-graining (CG) is a systematic reduction of the number of degrees of freedom (DOF) used to describe a system of interest. CG can be thought of as a projection on coarse-grained DOF and is therefore dependent on the functions used to represent the CG force field. In this work, we show that naive extensions of the coarse-grained force-field can result in unphysical parametrizations of the CG potential energy surface (PES). This issue can be elevated by coarse-graining the two- and three-body forces separately, which also helps to evaluate the importance of many-body interactions for a give…
Polymer-surface interactions are crucial to many biological processes and industrial applications. Here we propose a machine-learning method to connect a model polymer's sequence with its adhesion to decorated surfaces. We simulate the adhesive free energies of $20,000$ unique coarse-grained 1D sequential polymers interacting with functionalized surfaces and build support vector regression (SVR) models that demonstrate inexpensive and reliable prediction of the adhesive free energy as a function of the sequence. Our work highlights the promising integration of coarse-grained simulation with da…
Coupled length and time scales determine the dynamic behavior of polymers and underlie their unique viscoelastic properties. To resolve the long-time dynamics it is imperative to determine which time and length scales must be correctly modeled. Here we probe the degree of coarse graining required to simultaneously retain significant atomistic details and access large length and time scales. The degree of coarse graining in turn sets the minimum length scale instrumental in defining polymer properties and dynamics. Using linear polyethylene as a model system, we probe how coarse graining scale …
We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with a simple effective, coarse-grained off-lattice model to study the structure and the topology of the energy surface. The multicanonical method samples the whole rugged energy landscape, in particular the low-energy part, and enables one to better understand the critical behaviors and visualize the folding pathways of the considered protein model.
The paper constructs a coarse-grained model to investigate dry sliding friction of the body-centered-cubic Fe micron-scale system by smoothed particle hydrodynamics simulations and examines influences of the spring force on the characters of friction. The N_atom = 864 \times 10^12 atoms Fe system is coarse-grained into the two different simple-cubic particle systems, one of 432000 and the other of 16000 particles. From the detection of stick-slip motion, friction coefficient, dependence of friction coefficient on isotropy or anisotropy of the spring force and externally applied normal load, we…
Self-assembled linear structures like giant cylindrical micelles or discotic molecules in solution stacked in flexible columns are systems reminiscent of polydisperse polymer solutions.These supramolecular polymers have an equilibrium length distribution, the result of a competition between the random breakage of chains and the fusion of chains to generate longer ones. In the present work, we review the basic theoretical concepts of these ``equilibrium polymers" and some of the important results obtained by simulation approaches. We propose a new version of a mesoscopic model in continuous spa…
Several recently proposed semi--automatic and fully--automatic coarse--graining schemes for polymer simulations are discussed. All these techniques derive effective potentials for multi--atom units or super--atoms from atomistic simulations. These include techniques relying on single chain simulations in vacuum and self--consistent optimizations from the melt like the simplex method and the inverted Boltzmann method. The focus is on matching the polymer structure on different scales. Several ways to obtain a time-scale for dynamic mapping are discussed additionally. Finally, similarities to ot…
We extend our previously developed coarse-graining strategy for linear polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal crossover between the good-solvent and the Theta regimes. We consider the thermal crossover in the region in which tricritical effects can be neglected, i.e. not too close to the Theta point, for a wide range of chain volume fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling crossover functions for global properties of the solution are obtained by Mont…
Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.
We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and c…
We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where vesicles are subjected to compression between two plates or subjected to insertion into narrow channels. Analysis methods are developed for mapping particle configurations to continuum fields with spherical harmonics representations. Heterogeneous vesicles are found to exhibit rich behaviors where the heterogeneity can amplify surface two-point correlations,…
We present a theoretical approach which maps polymer blends onto mixtures of soft-colloidal particles. The analytical mesoscale pair distribution functions reproduce well data from united atom molecular dynamics simulations of polyolefin mixtures without fitting parameters. The theory exactly recovers the analytical expressions for density and concentration fluctuation structure factors of soft colloidal mixtures (liquid alloys).
We present a detailed derivation and testing of our approach to rescale the dynamics of mesoscale simulations of coarse-grained polymer melts (I. Y. Lyubimov et al. J. Chem. Phys. \textbf{132}, 11876, 2010). Starting from the first-principle Liouville equation and applying the Mori-Zwanzig projection operator technique, we derive the Generalized Langevin Equations (GLE) for the coarse-grained representations of the liquid. The chosen slow variables in the projection operators define the length scale of coarse graining. Each polymer is represented at two levels of coarse-graining: monomeric as …
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, …
We construct a coarse-grained (CG) model for dipalmitoylphosphatidylcholine (DPPC)/cholesterol bilayers and apply it to large-scale simulation studies of lipid membranes. Our CG model is a two-dimensional representation of the membrane, where the individual lipid and sterol molecules are described by point-like particles. The effective intermolecular interactions used in the model are systematically derived from detailed atomic-scale molecular dynamics simulations using the Inverse Monte Carlo technique, which guarantees that the radial distribution properties of the CG model are consistent wi…
Short fiber reinforced polymer composites have found extensive industrial and engineering applications owing to their unique combination of low cost, relatively easy processing and superior mechanical properties compared to their parent polymers. In this study, a coarse grained (CG) model of cross linked carbon nanotube (CNT) reinforced polymer matrix composites is developed. A characteristic feature of the CG model is the ability to capture the interactions between polymer chains, and nanotubes and polymer matrix. The dependence of the elastic properties of the composites on the mole fraction…
We perform kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts with an algorithm that is tractable even at low undercooling. The configuration of the non-crystallized chains under flow is computed with a recent non-linear tube model. Our simulations predict both enhanced nucleation and the growth of shish-like elongated nuclei for sufficiently fast flows. The simulations predict several experimental phenomena and theoretically justify a previously empirical result for the flow-enhanced nucleation rate. The simulations are highly pertinent to both the fundamental underst…
In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced polymer matrix composites is developed. A distinguishing feature of the CG model is the ability to capture interactions between polymer chains and nanotubes. The CG potentials for nanotubes and polymer chains are calibrated using the strain energy conservation between CG models and full atomistic systems. The applicability and efficiency of the CG model in predicting the elastic properties of CNT/polymer composites are evaluated through verification processes with molecular simulations. The simulation results reveal …
We present a coarse-grained model for linear polymers with a tunable number of effective atoms (blobs) per chain interacting by intra- and inter-molecular potentials obtained at zero density. We show how this model is able to accurately reproduce the universal properties of the underlying solution of athermal linear chains at various levels of coarse-graining and in a range of chain densities which can be widened by increasing the spatial resolution of the multiblob representation, i.e., the number of blobs per chain. The present model is unique in its ability to quantitatively predict thermod…
The J-integral is recognized as a fundamental parameter in fracture mechanics that characterizes the inherent resistance of materials to crack growth. However, the conventional methods to calculate the J-integral, which require knowledge of the exact position of a crack tip and the continuum fields around it, are unable to precisely measure the J-integral of polymer composites at the nanoscale. This work aims to propose an effective calculation method based on coarse-grained (CG) simulations for predicting the J-integral of carbon nanotube (CNT)/polymer composites. In the proposed approach, th…
We have developed a coarse-grained (CG) model of a polymer-clay system consisting of organically modified montmorillonite nanoclay as the nanoparticle in accordance with the MARTINI forcefield. We have used mechanical properties and cleavage free energy of clay particle to respectively parameterize bonded and nonbonded interaction parameters for an organically modified montmorillonite (oMMT) clay particle where intergallery Na+ ions are replaced by tetramethylammonium (TMA) ions. The mechanical properties were determined from the slope of stress-strain curve and cleavage free energy was determ…
By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show that, due to critical slowing down, an extremal autocorrelation time can also be considered as an indicator for the collapse transition that helps to locate the transition point. This is particularly useful for finite systems, where response quantities such as the specific heat do not necessarily exhibit clear indications for pronounced thermal activity.
We calculate the two, three, four, and five-body (state independent) effective potentials between the centers of mass (CM) of self avoiding walk polymers by Monte-Carlo simulations. For full overlap, these coarse-grained n-body interactions oscillate in sign as (-1)^n, and decrease in absolute magnitude with increasing n. We find semi-quantitative agreement with a scaling theory, and use this to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many-body potentials. We also derive effective {\em density dependent} 2-body potentials which exactly repro…
We use an "equation-free", coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable.
Coarse-Grained Molecular Dynamics Simulations of Oxidative Aging and Stabilization in Polymer Melts with Primary Antioxidants: Effects of Antioxidant Concentration and Molecular Architecture
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to design well-founded multi-scale modeling tools that can link microscopic models with macroscopic constitutive equations. Such multi-scale modeling tools benefit from recently proposed approaches for static coarse graining which are mainly built on potentials of mean force. For dynamical properties, however, coarse-grained models need to account for dissipative e…
